Extremely difficult PG

Originally posted by SwissGambit
5...a1R 6...Rxc1 7...Rxd1+ 8.Kxd1 12.Kb3 Qa1 13...Qxf1 14...Qa1 15...Qa5 16.Ra1 Ba3 17.Ka2 21.Ke1 Qxa1# - the sequence is fast enough.

Black's moves: 7 for Pa7, 7 for Qd8, 3 for Bd4, 5 for other pieces = 22 total moves. Bust!

Edit: I crossed Item #5 off the list too soon. I cannot just assume the promoted piece that takes c1 gets captured. Maybe it's still on the board. More next post....

Ok, let's analyze cases where the promoted piece is still on the board in item #5.

A promoted Q remaining on board is obviously slower than the previous sequence [she still has to clear the a-file after taking c1 AND the other Q has to come in].

With promoted R:

5...a1R 6...Rxc1 7...Ra1 8...R1a6 9.Qa1 Rah6 14.Kb3 Qxa1 15...Qxf1 16...Qa1 17...Qa5 18...Ba3 19.Ka2 23.Ke1 - abysmally slow.

With promote N:
5...a1N 7...Nxc1 8...N~ 9.Qa1 14.Kb3 Qxa1 turns out just like the promoted R scheme.

NOW we can cross Item #5 off the list.

Originally posted by Jirakon
6. Promoted pawn takes c1, rook takes f1.

a) promoted R takes c1 and dies:
5...a1R 6...Rxc1 7...Rxd1+ 8.Kxd1 12.Kb3 Ra1 13...Rxf1 14...Ra1 15...Raa6 16.Ra1 Rah6 17.Ka2 21.Ke1 is fast enough. Black needs 7 for Pa7 + 5 for Rh6 + 8 for other pieces = 20 total, giving us one spare move to play with. The problem is that Black needs to shield on the a-file at move 11 or so, but we can't play ...e6 until the R is on h6, and any other shield besides Ba3 or Bc5-a7 requires two extra moves for Black.

b) promote R takes c1 and lives:
5...a1R 6...Rxc1 7...Ra1 8...R1a6 9.Qa1 14.Kb3 Rxa1 15...Rxf1 16.Ka2 Ra1+ 17.Rxa1 18.Kb1 21.Ke1 is fast enough. Black needs 9 for Pa7 + 3 for Ra8 + 8 for other pieces = 20 moves. We still have a move to spare for Black. This scheme has the further advantage of allowing ...e6 on move 10, opening up the Bf8 diagonal so it can shield.

White needs 10 for K, 1 for Rh1-a1, 3 for Ng1-b3 [to help bPa7 promote] = 14 moves. This leaves 7 spare, most of which will be used to take out the bPh7, which never moves, because Black must use his one spare move to shield on the a-file.

Originally posted by SwissGambit
I'm afraid it says more about the level of interest in this problem 😕

Pessimist. 😕

Originally posted by curseknight
Pessimist. 😕

However, I would love to be proven wrong on this issue. Scheme 6b) I left open, as it looks very promising. Let us see if someone will explore it further.

I see how 6b) cooks the authors original proof game, but since the rook can't h7 escape in this position, and the knight can't get to a square on the queen's path with one move from h7, I don't think 6b) works.

Originally posted by Jirakon
the knight can't get to a square on the queen's path with one move from h7

False!

I guess I should be more specific. After 8 Nxh7 (which does not have a unique path anyway), black plays 8...R1a6, then white's moves must be with the king and queen until move 14 Kb2. During this time, the black f bishop must get to a1, so the 6th rank will be blocked by a pawn. It takes moves 9...Rh6, 10...e6, and 11...Ba3 to get it there, and it can't go to c5 until after 13 Ka2. So black's 12th move can only be 12...d5, blocking the 5th rank as well (black can't have moved the queen, as the white knight has yet to move to a capturable square). The black king is already blocking the 8th rank. Since the 5th, 6th, and 8th ranks are the only ones that the knight can move to, the queen can't capture it and get to a1 in three moves.

EDIT: Actually, d5 doesn't have to be the 12th move necessarily, but it does have to be among moves 9-12.

Originally posted by Jirakon
I guess I should be more specific. After 8 Nxh7 (which does not have a unique path anyway), black plays 8...R1a6, then white's moves must be with the king and queen until move 14 Kb2. During this time, the black f bishop must get to a1, so the 6th rank will be blocked by a pawn. It takes moves 9...Rh6, 10...e6, and 11...Ba3 to get it there, and it can't go t ...[text shortened]... d5 doesn't have to be the 12th move necessarily, but it does have to be among moves 9-12.

It's not so much that your reasoning is wrong, it's that you're missing another possible line of play.

OK, time for another hint.

Look for another shield besides ...Ba3.

Oooooohhhhh... SOLV'D, though it probably doesn't count for much now.

Originally posted by Jirakon
Oooooohhhhh... SOLV'D, though it probably doesn't count for much now.

CONFIRM'D